User:Polygon/Page for testing: Difference between revisions

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Polygon (talk | contribs)
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Polygon (talk | contribs)
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Placeholder
<pre>
{| class="wikitable"
Let's rewrite the first rule as:
!Standard format
A(a, b) --> A(2a + 4, b - a - 3) if b >= a + 3
!Approximate score/runtime
Then, after n applications of rule 1 (assuming b is large enough):
|-
A(a, b) --> A(2^n * a + 2^(n + 2) - 4, b - 2^n * a + a - 2^(n + 2) + n + 4)
|{{TM|1RB1RE_1LC1LF_1RD0LB_1LE0RC_1RA0LD_1RZ1LC}}
Considering that a is always set to 4 when leaving B, this simplifies to:
|10 ↑↑ 5.56344
A(4, b) --> A(2^(n + 3) - 4, b - 2^(n + 3) + n + 8)
|-
Now consider the halting configuration: A(a, a + 1):
|{{TM|1RB0LE_0RC1RA_0LD1RF_1RE0RB_1LA0LC_0RD1RZ}}
So, for this to be in a halting configuration, the following must be true:
|10 ↑↑ 5.12468
2^(n+3)-4 + 1 = b-2^(n+3)+n+8
|-
This simplifies to:
|{{TM|1RB0RF_1LC1LB_0RE0LD_0LC0LB_0RA1RE_0RD1RZ}}
b = 2^(n+4)-n-11
|10 ↑↑ 5.03230
</pre>
|-
|{{TM|1RB1LA_1LC0RF_1LD1LC_1LE0RE_0RB0LC_1RZ1RA}}
|10 ↑↑ 4.91072
|-
|{{TM|1RB0LE_1LC1RA_1RE0LD_1LC1LF_1LA0RC_1RZ1LC}}
|10 ↑↑ 3.33186
|-
|{{TM|1RB1RF_1LC1RE_0LD1LB_1LA0RA_0RA0RB_1RZ0RD}}
|10 ↑↑ 3.31128
|-
|{{TM|1RB0LF_1LC0RA_1RD0LB_1LE1RC_1RZ1LA_1LA1LE}}
|10 ↑↑ 3.18855
|}

Revision as of 20:33, 25 October 2025

Let's rewrite the first rule as:
A(a, b) --> A(2a + 4, b - a - 3) if b >= a + 3
Then, after n applications of rule 1 (assuming b is large enough):
A(a, b) --> A(2^n * a + 2^(n + 2) - 4, b - 2^n * a + a - 2^(n + 2) + n + 4)
Considering that a is always set to 4 when leaving B, this simplifies to:
A(4, b) --> A(2^(n + 3) - 4, b - 2^(n + 3) + n + 8)
Now consider the halting configuration: A(a, a + 1):
So, for this to be in a halting configuration, the following must be true:
2^(n+3)-4 + 1 = b-2^(n+3)+n+8
This simplifies to:
b = 2^(n+4)-n-11
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